A note on the uniqueness of the closed orbit of the FitzHugh-Nagumo system
Author:
Makoto Hayashi
Journal:
Quart. Appl. Math. 58 (2000), 171-176
MSC:
Primary 34C25; Secondary 34C60
DOI:
https://doi.org/10.1090/qam/1739043
MathSciNet review:
MR1739043
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Abstract: A parameter range for which the ordinary differential equations governing the FitzHugh nerve system have a unique nontrivial closed orbit is given. It is wider than those already known.
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R. FitzHugh, Impulses and physiological states in theoretical models of nerve membrane, Biophys. J. 1, 445–466 (1961)
M. Hayashi, On the uniqueness of the closed orbit of FitzHugh-Nagumo system, Math. Japon. 46 (2), 331–336 (1997)
M. Hayashi, On the uniqueness of the closed orbit of the Liénard system, Math. Japon. 46 (3), 371–376 (1997)
E. Kaumann and U. Staude, Uniqueness and nonexistence of limit cycles for the FitzHugh equation, Lecture Notes in Math. 1017, Springer-Verlag, New York, 1983, pp. 313–321
J. Nagumo, S. Arimoto, and S. Yoshizawa, An active pulse transmission line simulating nerve axon, Proc. IRE 50, 2061–2070 (1962)
J. Sugie, Nonexistence of periodic solutions for the FitzHugh nerve system, Quart. Appl. Math. 49, 543–554 (1991)
S. A. Treskov and E. P. Volokitin, On existence of periodic orbits for the FitzHugh nerve system, Quart. Appl. Math. 54, 601–607 (1996)
X. Zeng, On the uniqueness of limit cycle of Liénard’s equation, Scientia Sinica (Series A) 25, 583–592 (1982)
X. Zeng, Z. Zhang, and S. Gao, On the uniqueness of the limit cycle of the generalized Liénard equation, Bull. London Math. Soc. 26, 213–247 (1994)
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© Copyright 2000
American Mathematical Society
